Coalgebraic Bisimulation-Up-To

  • Jurriaan Rot
  • Marcello Bonsangue
  • Jan Rutten
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7741)


Bisimulation-up-to enhances the bisimulation proof method for process equivalence. We present its generalization from labelled transition systems to arbitrary coalgebras, and show that for a large class of systems, enhancements such as bisimulation up to bisimilarity, up to equivalence and up to context are sound proof techniques. This allows for simplified bisimulation proofs for many different types of state-based systems.


Regular Expression Label Transition System Stream System Equivalence Closure Follow Diagram Commute 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Aczel, P., Mendler, N.: A Final Coalgebra Theorem. In: Dybjer, P., Pitts, A.M., Pitt, D.H., Poigné, A., Rydeheard, D.E. (eds.) Category Theory and Computer Science. LNCS, vol. 389, pp. 357–365. Springer, Heidelberg (1989)CrossRefGoogle Scholar
  2. 2.
    Bartels, F.: On generalised coinduction and probabilistic specification formats. PhD thesis, CWI, Amsterdam (2004)Google Scholar
  3. 3.
    Bonchi, F., Bonsangue, M., Boreale, M., Rutten, J., Silva, A.: A coalgebraic perspective on linear weighted automata. Inf. Comput. 211, 77–105 (2012)MathSciNetzbMATHCrossRefGoogle Scholar
  4. 4.
    Bonchi, F., Pous, D.: Checking NFA equivalence with bisimulations up to congruence. In: POPL (to appear, 2013)Google Scholar
  5. 5.
    Gumm, H.P.: Elements of the general theory of coalgebras. In: LUATCS 1999 Rand Afrikaans University, South Africa (1999)Google Scholar
  6. 6.
    Klin, B.: Bialgebras for structural operational semantics: An introduction. TCS 412(38), 5043–5069 (2011)MathSciNetzbMATHCrossRefGoogle Scholar
  7. 7.
    Lenisa, M.: From set-theoretic coinduction to coalgebraic coinduction: some results, some problems. ENTCS 19, 2–22 (1999)MathSciNetGoogle Scholar
  8. 8.
    Milner, R.: Calculi for synchrony and asynchrony. TCS 25, 267–310 (1983)MathSciNetzbMATHCrossRefGoogle Scholar
  9. 9.
    Pous, D., Sangiorgi, D.: Enhancements of the bisimulation proof method. In: Advanced Topics in Bisimulation and Coinduction, pp. 233–289. Cambridge University Press (2012)Google Scholar
  10. 10.
    Rutten, J.: Automata and Coinduction (An Exercise in Coalgebra). In: Sangiorgi, D., de Simone, R. (eds.) CONCUR 1998. LNCS, vol. 1466, pp. 194–218. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  11. 11.
    Rutten, J.: Universal coalgebra: a theory of systems. TCS 249(1), 3–80 (2000)MathSciNetzbMATHCrossRefGoogle Scholar
  12. 12.
    Rutten, J.: Behavioural differential equations: a coinductive calculus of streams, automata, and power series. TCS 308(1-3), 1–53 (2003)MathSciNetzbMATHCrossRefGoogle Scholar
  13. 13.
    Sangiorgi, D.: On the bisimulation proof method. Math. Struct. Comp. Sci. 8(5), 447–479 (1998)MathSciNetzbMATHGoogle Scholar
  14. 14.
    Zhou, X., Li, Y., Li, W., Qiao, H., Shu, Z.: Bisimulation Proof Methods in a Path-Based Specification Language for Polynomial Coalgebras. In: Ueda, K. (ed.) APLAS 2010. LNCS, vol. 6461, pp. 239–254. Springer, Heidelberg (2010)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Jurriaan Rot
    • 1
    • 2
  • Marcello Bonsangue
    • 1
    • 2
  • Jan Rutten
    • 2
    • 3
  1. 1.LIACSLeiden UniversityThe Netherland
  2. 2.Centrum Wiskunde en InformaticaThe Netherland
  3. 3.Radboud University NijmegenThe Netherland

Personalised recommendations